1. Field of the Invention
This invention relates generally to a method and apparatus for determining the horizontal and vertical resistivities and the relative dip angle of a borehole in an electrically anisotropic earth formation. More specifically, this invention relates to an electromagnetic wave induction technique for measuring resistivity using a tool having an antenna that is disposed within a plane which is inclined with respect to a plane that is normal to the axis of the tool.
2. Description of the Related Art
In the field of petroleum well drilling and logging, electromagnetic wave resistivity sensors are frequently used to provide an indication of the electrical resistivity of rock formations surrounding an earth borehole. Such information regarding resistivity is useful in ascertaining the presence or absence of hydrocarbons. A typical electromagnetic wave resistivity tool comprises a transmitter antenna and a pair of receiver antennas located at different distances from the transmitter antenna along the axis of the tool. The transmitter antenna is used to transmit electromagnetic waves into the surrounding formation. In turn, the magnetic field in the formation induces an electrical voltage in each receiver antenna. Due to geometric spreading and absorption by the surrounding earth formation, the induced voltages in the two receiving antennas have different phases and amplitudes. Experiments have shown that the phase difference (.PHI.) and amplitude ratio (attenuation, A) of the induced voltages in the receiver antennas are indicative of the resistivity of the formation. The point in the formation (as defined by a radial distance from the tool axis) to which such a resistivity measurement pertains is a function of the frequency of the transmitter and the distance from the transmitter to the mid-point between the two receivers. Thus, one may achieve multiple radial depths of investigation of resistivity either by providing multiple transmitters at different distances from the receiver pair or by operating a single transmitter at multiple frequencies.
If a formation is electrically isotropic, the resistivities measured at the various depths of investigation by such an electromagnetic wave resistivity tool will be the same. However, if the resistivities corresponding to the various depths of investigation are different, such differences indicate that the formation being measured is electrically anisotropic. In electrically anisotropic formations, the anisotropy is generally attributable to extremely fine layering during the sedimentary build-up of the formation. Hence, in a formation coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities R.sub.x and R.sub.y in directions x and y, respectively, are the same, but resistivity R.sub.z in the z direction is different from R.sub.x and R.sub.y. Thus, the resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is known as the horizontal resistivity, R.sub.h, and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is known as the vertical resistivity, R.sub.v. The index of anisotropy, .alpha., is defined as .alpha.=[R.sub.v /R.sub.h ].sup.1/2.
The relative dip angle, .theta., is the angle between the borehole axis (tool axis) and the normal to the plane of the formation. If the axis of an electromagnetic wave resistivity tool is perpendicular to the plane of an anisotropic formation (i.e., .theta.=0.degree.), both the phase shift and amplitude attenuation measurements reflect only the horizontal resistivity. However, if the axis of the tool is inclined with respect to the normal of the formation plane (i.e., for non-zero relative dip angle), the rock anisotropy affects the resistivity derived from phase shift measurements ("phase shift resistivity" or R.sub..PHI.) differently than it affects the resistivity derived from amplitude attenuation measurements ("amplitude attenuation resistivity" or R.sub.A). For small relative dip angles (e.g., .theta. less than about 45.degree.), the difference between phase shift and amplitude attenuation resistivities is relatively small. However, this difference becomes significant for relative dip angles greater than about 50.degree., and the difference is large for horizontal boreholes (i.e., .theta.=90.degree.).
Before the present invention, practitioners in the art have used a number of techniques to determine the anisotropy of earth formations, most of which involve the use of coil antennas to measure resistivity. However, each of the existing techniques suffers from one or more disadvantages. For example, U.S. Pat. No. 4,980,643, issued Dec. 25, 1990 to Gianzero and Su, teaches the use of additional receiver coils oriented differently from (not co-axial with) conventional receiver coils to detect skew signals induced by skewness in the magnetic field pattern in the presence of asymmetrical formations. The axis of such additional receiver coils according to the '643 patent is preferably orthogonal to that of the conventional receiver coils, which are co-axial with the tool axis. However, such orthogonal coil (antenna) configurations are not generally considered practical for a measuring while drilling (MWD) or logging while drilling (LWD) tool because, if the coil is located in the interior of the tool, the presence of the coil necessitates a non-conventional mud flow path and decreases the mechanical strength of the tool. If, on the other hand, the additional coil is located on the exterior of the tool, the coil is susceptible to damage by formation cuttings in the return mud flow.
Similarly, U.S. Pat. No. 5,329,448, issued Jul. 12, 1994 to Rosthal, discloses a method and apparatus for determining the horizontal and vertical resistivities of an earth formation using an iterative error minimization technique. However, the '448 patent, which discloses a conventional antenna configuration in which the transmitter and receiver coils are aligned co-axially with the tool, does not provide a way to determine the relative dip angle. Instead, the relative dip angle must be obtained from another measurement source or from prior knowledge of the formation. Likewise, U.S. Pat. No. 5,656,930, issued Aug. 12, 1997 to Hagiwara, discloses a method for determining the anisotropic properties of subterranean formations comprising thinly laminated sand/shale sequences using an induction logging tool. However, like the '448 patent, the method of the '930 patent requires the derivation of the relative dip angle from another measurement.
In a technical paper entitled "A New Method to Determine Horizontal Resistivity in Anisotropic Formations Without Prior Knowledge of Relative Dip," 37th SPWLA 37th Annual Logging Symposium, New Orleans, Jun. 16-19, 1996, Hagiwara discloses a method to determine the horizontal resistivity for deviated boreholes or dipping formations using two conventional induction-type resistivity measurements. However, Hagiwara's method does not provide the relative dip angle. To obtain the relative dip angle, the formation anisotropy must be known. Moreover, Hagiwara showed that, for conventional induction logging tools (in which the transmitter and receiver antennas are oriented co-axially with the tool), it is impossible to obtain all three parameters (horizontal resistivity, vertical resistivity, and relative dip angle) simultaneously. The reason such a simultaneous solution is not possible using conventional induction logging tools is that, in the response of such tools, the vertical resistivity and the relative dip angle are coupled (i.e., they are not independent).
In European Patent Application No. 97118854.5 by Wu, published May 6, 1998, Wu discloses a method and apparatus for determining horizontal conductivity, vertical conductivity, and relative dip angle during a drilling operation. If the relative dip angle is unknown, Wu's technique involves the formulation of a relationship between the dielectric constants of the formation to the anisotropic conductivities of the formation. However, in the proof by Hagiwara mentioned above, the dielectric constants are assumed quantities, and their contribution to the phase shift resistivity is minimal. Therefore, even if the dielectric constants are known, the vertical resistivity and the relative dip angle are still coupled and do not allow for a simultaneous solution.
It would, therefore, be a significant advancement in the art to provide an improved method and apparatus for simultaneously determining the horizontal resistivity, vertical resistivity, and relative dip angle in a MWD or LWD mode or operation.